Numerical Analysis of Different Influencing Factors on the In-Plane Failure Mode of Unreinforced Masonry (URM) Structures
Abstract
:1. Introduction
2. Judgement of Failure Mode of Masonry
2.1. Judgement Procedures of Failure Mode
2.2. Analysis for Specific Case
3. Main Factors Affecting Failure Mode: Numerical Simulation
3.1. Model Design
3.2. Mechanical Parameters
3.3. Constraints and Interactions
3.4. Load Actions
4. Discussion of Numerical Results
4.1. Effects of Aspect Ratio and Stiffness Ratio
4.2. Effects of Vertical Load
5. Conclusions
- (1)
- The stress value of each model gradually decreased from first floor to third floor, demonstrating the fact that the damage degree of masonry wall gradually weakened from the bottom floor to the top floor.
- (2)
- The simulation results exhibited that the cracks and damages of FEMs initially emerged at the edge of the openings, and further elongated and widened along the adjacent parts, which were consistent with the actual earthquake damage phenomenon.
- (3)
- The failure modes of models with smaller aspect ratio of the pier showed a similar regulation, which was that the failure modes of models transferred from pier failure mode to mixed failure mode and from mixed failure mode to spandrel failure mode with the gradual increase in stiffness ratio of pier to spandrel. However, pier failure mode occurred for all models with a larger aspect ratio of pier only, regardless of whether the stiffness ratio of pier to spandrel increased or decreased.
- (4)
- Under the identical aspect ratio of pier, the failure modes of the models altered regularly with the increase in vertical load, which transferred from pier failure to mixed failure, and from mixed failure to spandrel failure.
- (5)
- Considering the failure mechanism of masonry structure “strong pier and weak spandrel” rather than “strong spandrel and weak pier”, the aspect ratio of the pier of masonry structures should not exceed 1.0, and the stiffness ratio of pier to spandrel should be in the range of 1.0–2.0.
- (6)
- Vertical load has a significant effect on the failure mode of masonry structures. Generally, assuming that the vertical load of each floor is 0.1 MPa, the vertical load that can lead to the “strong pier and weak spandrel” failure mode of n-floors masonry structures shall not be less than (0.1 × n) MPa.
- (7)
- The numerical simulation in this paper was carried out through the overall model. The anisotropy of brick and mortar was ignored, and the seismic action suffered by masonry buildings was not fully considered. Thus, a separated model should be established to obtain more reasonable simulation results.
- (8)
- The finite element model used in this paper did not pay attention to the influence of ring beam, structural column and floor, and so on. Therefore, the finite element model considering various influencing factors should be established, so that the stress mechanism and failure mode of masonry buildings can be further discussed and analyzed.
Author Contributions
Funding
Conflicts of Interest
References
- Ma, P.; Xin, R.; Yao, J. Assessment of failure mode and seismic performance of damaged masonry structures retrofitted with grout-injected ferrocement overlay reinforcement (GFOR). Constr. Build. Mater. 2021, 305, 124778. [Google Scholar] [CrossRef]
- Xin, R.; Ma, P. Experimental investigation on the in-plane seismic performance of damaged masonry walls repaired with grout-injected ferrocement overlay. Constr. Build. Mater. 2021, 282, 122565. [Google Scholar] [CrossRef]
- Rossetto, T.; Peiris, N. Observations of damage due to the Kashmir earthquake of October 8, 2005 and study of current seismic provisions for buildings in Pakistan. Bull. Earthq. Eng. 2009, 7, 681–699. [Google Scholar] [CrossRef]
- Zhao, B.; Taucer, F.; Rossetto, T. Field investigation on the performance of building structures during the 12 May 2008 Wenchuan earthquake in China. Eng. Struct. 2009, 31, 1707–1723. [Google Scholar] [CrossRef]
- Zhou, D.; Lei, Z.; Wang, J. In-plane behavior of seismically damaged masonry walls repaired with external BFRP. Compos. Struct. 2013, 102, 9–19. [Google Scholar] [CrossRef]
- Kadam, S.B.; Singh, Y.; Li, B. Strengthening of unreinforced masonry using welded wire mesh and micro-concrete–behaviour under in-plane action. Constr. Build. Mater. 2014, 54, 247–257. [Google Scholar] [CrossRef]
- Ismail, N.; Ingham, J.M. In-plane and out-of-plane testing of unreinforced masonry walls strengthened using polymer textile reinforced mortar. Eng. Struct. 2016, 118, 167–177. [Google Scholar] [CrossRef]
- Kevin, W.; Dmytro, D.; Ivan, G.; Hossein, D.; Jason, I. Predicted versus experimental out-of-plane force-displacement behaviour of unreinforced masonry walls. Structures 2018, 15, 292–306. [Google Scholar] [CrossRef]
- Pradhan, B.; Zizzo, M.; Sarhosis, V.; Cavaleri, L. Out-of-plane behaviour of unreinforced masonry infill walls: Review of the experimental studies and analysis of the influencing parameters. Structures 2021, 33, 4387–4406. [Google Scholar] [CrossRef]
- Mojsilović, N. Strength of masonry subjected to in-plane loading: A contribution. Int. J. Solids Struct. 2011, 48, 865–873. [Google Scholar] [CrossRef] [Green Version]
- Plevris, V.; Asteris, P.G. Modeling of masonry failure surface under biaxial compressive stress using neural networks. Constr. Build. Mater. 2014, 55, 447–461. [Google Scholar] [CrossRef]
- Naraine, K.; Sinha, S. Cyclic behavior of brick masonry under biaxial compression. J. Struct. Eng. 1991, 117, 1336–1355. [Google Scholar] [CrossRef]
- Syrmakezis, C.A.; Chronopoulos, M.P.; Sophocleou, A.A. Structural analysis methodology for historical buildings. In Structural Studies of Historical Buildings IV; Computational Mechanics Publications: Lisbon, Portugal, 1995; pp. 373–382. [Google Scholar]
- GB/T 50129–2011; Standard for Test Method of Basic Mechanics Properties of Masonry. China Architecture and Building Press: Beijing, China, 2011.
- Asteris, P.G. Unified yield surface for the nonlinear analysis of brittle anisotropic materials. Nonlinear Sci. Lett. A 2013, 4, 46–56. [Google Scholar]
- Page, A.W. The biaxial compressive strength of brick masonry. Proc. Inst. Civ. Eng. 1981, 71, 893–906. [Google Scholar] [CrossRef]
- Samarasinghe, W. The In-Plane Failure of Brickwork. Ph.D. Thesis, University of Edinburgh, Edinburgh, UK, 1980. [Google Scholar]
- Dhanasekar, M.; Page, A.; Kleeman, P. The failure of brick masonry under biaxial stresses. Ice Proc. 1985, 79, 295–313. [Google Scholar] [CrossRef]
- Tassios, T.P.; Vachliotis, C. Failure of masonry under heterosemous biaxial stresses. In Structural Conservation of Stone Masonry; International Centre for the Study of the Preservation and the Restoration of Cultural Property: Rome, Italy, 1990; pp. 273–282. [Google Scholar]
- Liu, L.P.; Tang, D.X.; Tian, Y.B. Experimental study of anisotropic strength characteristics of grouted concrete block masonry. J. Build. Struct. 2005, 26, 91–95. [Google Scholar]
- Liang, J.G.; Fang, L. Yield criterion and calculation of shear strength for brick masonry walls. Chin. J. Civ. Eng. 2010, 43, 43–46. [Google Scholar]
- Xin, R.; Yao, J.; Zhao, Y. Experimental research on masonry mechanics and failure under biaxial compression. Struct. Eng. Mech. 2017, 61, 167–175. [Google Scholar] [CrossRef]
- Ma, P.F. Experimental Study on Seismic Behavior of Reinforced Masonry Structure Based on Spandrel Failure Mode. Master’s Thesis, Xi’an University of Architecture and Technology, Xi’an, China, 2019. [Google Scholar]
- EN 1998-1; Eurocode 8–Design of Structures for Earthquake Resistance—Part 1: General Rules, Seismic Actions and Rules for Buildings. European Standard NFEN; European Committee for Standardization: Brussels, Belgium, 1998.
- FEMA 356; Prestandard for the Seismic Rehabilitation of Existing Structures. FEMA: Washington, DC, USA, 2000.
- Lagomarsino, S.; Penna, A.; Galasco, A.; Cattari, S. TREMURI program: An equivalent frame model for the nonlinear seismic analysis of masonry buildings. Eng. Struct. 2013, 56, 1787–1799. [Google Scholar] [CrossRef]
- D’Altri, A.M.; Sarhosis, V.; Milani, G.; Rots, J.; Cattari, S.; Lagomarsino, S.; Sacco, E.; Tralli, A.; Castellazzi, G.; de Miranda, S. Modeling strategies for the computational analysis of unreinforced masonry structures: Review and classification. Arch. Comput. Methods Eng. 2019, 27, 1153–1185. [Google Scholar] [CrossRef]
- Rinaldin, G.; Amadio, C.; Gattesco, N. Review of experimental cyclic tests on unreinforced and strengthened masonry spandrels and numerical modelling of their cyclic behaviour. Eng. Struct. 2017, 132, 609–623. [Google Scholar] [CrossRef]
- Abrams, D.P. Seismic response patterns for URM buildings. J. Mas Soc. 2000, 18, 71–78. [Google Scholar]
- GB 50203–2011; Code for Design of Masonry Structures. China Architecture and Building Press: Beijing, China, 2011.
- Ewing, R.D.; Kariotis, J.C.; Mustapha, A. A computer program for the nonlinear, dynamic, analysis of lumped parameter models. In US–Japan Coordinated Program for Masonry Building Research; National Technical Information Service: Springfield, VA, USA, 1988. [Google Scholar]
- Parisi, F.; Lignola, G.P.; Augenti, N.; Prota, A.; Manfredi, G. Rocking response assessment of in-plane laterally-loaded masonry walls with openings. Eng. Struct. 2013, 56, 1234–1248. [Google Scholar] [CrossRef]
- Gattesco, N.; Clemente, I.; Macorini, L. Experimental investigation on the behaviour of spandrels in ancient masonry buildings. In Proceedings of the 14th World Conference on Earthquake Engineering, Beijing, China, 12–17 October 2008. [Google Scholar]
- Parisi, F.; Augenti, N.; Prota, A. Implications of the spandrel type on the lateral behavior of unreinforced masonry walls. Earthq. Eng. Struct. Dyn. 2014, 43, 1867–1887. [Google Scholar] [CrossRef]
- Mahdavi, N.; Ahmadi, H.R.; Mahdavi, H. A comparative study on conventional push-over analysis method and incremental dynamic analysis (IDA) approach. Sci. Res. Essays 2012, 7, 751–773. [Google Scholar]
- Ahmadi, H.R.; Namdari, N.; Cao, M. Seismic investigation of pushover methods for concrete piers of curved bridges in plan. Comput. Concr. 2019, 23, 1–10. [Google Scholar]
- Ahmadi, H.R.; Mahdavi, N.; Bayat, M. Applying adaptive pushover analysis to estimate incremental dynamic analysis curve. J. Earthq. Tsunami 2020, 14, 2050016. [Google Scholar] [CrossRef]
- Knox, C.L.; Dizhur, D.; Ingham, J.M. Experimental cyclic testing of URM pier-spandrel substructures. J. Struct. Eng. 2016, 143, 04016177. [Google Scholar] [CrossRef]
- Yang, W.Z. Constitutive relationship model for masonry materials in compression. Build. Struct. 2008, 10, 80–82. [Google Scholar]
- Yan, F. Study on the Whole Mechanics of Wall Structure of Masonry Structure. Master’s Thesis, Xi’an University of Architecture and Technology, Xi’an, China, 2017. [Google Scholar]
- GB/T 2542–2012; Test Method for Wall Bricks. China Architecture and Building Press: Beijing, China, 2012.
- GB/T 25181–2019; Ready-Mixed Mortar. China Architecture and Building Press: Beijing, China, 2019.
- Gattesco, N.; Amadio, C.; Bedon, C. Experimental and numerical study on the shear behavior of stone masonry walls strengthened with GFRP reinforced mortar coating and steel-cord reinforced repointing. Eng. Struct. 2015, 90, 143–157. [Google Scholar] [CrossRef] [Green Version]
- Xia, Y.X. Study on Seismic Damage Mechanism of Masonry Spandrel Walls. Master’s Thesis, Institute of Engineering Mechanics, China Seismological Bureau, Harbin, China, 2011. [Google Scholar]
- GB 50009–2012; Load Code for the Design of Building Structures. China Architecture and Building Press: Beijing, China, 2012.
- Hadzima-Nyarko, M.; Čolak, S.; Bulajić, B.; Ademović, N. Assessment of selected models for FRP-retrofitted URM walls under in-plane loads. Buildings 2021, 11, 559. [Google Scholar] [CrossRef]
- Cavaleri, L.; Di Trapani, F.; Asteris, P. Infilled frames and equivalent struts: An approach considering the effects of openings and vertical loads. J. Struct. Infrastruct. Eng. 2015, 12, 551–566. [Google Scholar]
Loading Displacement | Location of Data Extraction | σx | σy | τxy |
---|---|---|---|---|
4 mm | spandrel (2nd) | −0.142453 | −0.030303 | 0.092791 |
pier (1st) | −0.024440 | −0.318460 | 0.091702 |
Model | Width × Height of Pier | Width × Height of Spandrel | η | ρ# |
---|---|---|---|---|
M1-1 | 1800 × 1500 | 435 × 1500 | 0.8 | 0.5 |
M2-1 | 1500 × 1500 | 750 × 1500 | 1.0 | 0.5 |
M3-1 | 1000 × 1800 | 1550 × 1200 | 1.8 | 0.5 |
Parameters | ρ = 0.5 | ρ = 0.75 | ρ = 1.0 | ρ = 1.25 | ρ = 1.5 | ρ = 1.75 | ρ = 2.0 | Models |
---|---|---|---|---|---|---|---|---|
η = 0.8 | P | P | M | M | S | S | S * | M1-1~M1-7 |
η = 1.0 | P | P | M | M | M | S | S | M2-1~M2-7 |
η = 1.8 | P | P | P | P | P | P | P | M3-1~M3-7 |
Models | ρ = 0.5 | ρ = 0.75 | ρ = 1.0 | ρ = 1.25 | ρ = 1.5 | ρ = 1.75 | ρ = 2.0 |
---|---|---|---|---|---|---|---|
σ = 0.3 MPa | P | P | M | M | M | S | S |
σ = 0.6 MPa | M | M | M | S | S | S | S |
Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. |
© 2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).
Share and Cite
Ma, P.; Yao, J.; Hu, Y. Numerical Analysis of Different Influencing Factors on the In-Plane Failure Mode of Unreinforced Masonry (URM) Structures. Buildings 2022, 12, 183. https://doi.org/10.3390/buildings12020183
Ma P, Yao J, Hu Y. Numerical Analysis of Different Influencing Factors on the In-Plane Failure Mode of Unreinforced Masonry (URM) Structures. Buildings. 2022; 12(2):183. https://doi.org/10.3390/buildings12020183
Chicago/Turabian StyleMa, Pengfei, Jitao Yao, and Yukun Hu. 2022. "Numerical Analysis of Different Influencing Factors on the In-Plane Failure Mode of Unreinforced Masonry (URM) Structures" Buildings 12, no. 2: 183. https://doi.org/10.3390/buildings12020183